#### Answer

$\dfrac{a-5b}{a^{2}+ab}\cdot\dfrac{b^{2}-a^{2}}{10b-2a}=\dfrac{a-b}{2a}$

#### Work Step by Step

$\dfrac{a-5b}{a^{2}+ab}\cdot\dfrac{b^{2}-a^{2}}{10b-2a}$
Factor both rational expressions completely:
$\dfrac{a-5b}{a^{2}+ab}\cdot\dfrac{b^{2}-a^{2}}{10b-2a}=\dfrac{a-5b}{a(a+b)}\cdot\dfrac{(b-a)(b+a)}{2(5b-a)}=...$
Evaluate the product:
$...=\dfrac{(a-5b)(b-a)(a+b)}{2a(a+b)(5b-a)}=...$
Change the sign of the numerator and the denominator:
$...=\dfrac{-(a-5b)(b-a)(a+b)}{-2a(a+b)(5b-a)}=\dfrac{(a-5b)(a-b)(a+b)}{2a(a+b)(a-5b)}=...$
Simplify by removing the factors that appear both in the numerator and in the denominator:
$...=\dfrac{a-b}{2a}$